HYACINTHOS 20428

Dear All My Friends,
 
O, H, K, L are circumcenter, orthocenter, symmedian and de
Longchamps points of reference triangle ABC. Suppose A'B'C' is orthic triangle
of ABC.
Denote A'', B'', C'' as midpoints of LA', LB', LC'
respectively.
 
Results:
1). A''B''C'' and ABC are perspective at perspector P with
barycentrics:
 
SA/(SA^2 + b^2*c^2)  :  :
 
Search value: +10.28933674999
P is on Jerabek hyperbola and P = gX(1593)
 
2). A''B''C'' and circumcevian triangle of O are perspective
at perspector Q with barycentrics:
 
SA*(a^4 - SB*SC)  :  :
 
Search value: +7.66243640106
Q is reflection of orthocenter H in symmedian point K.
 
P and Q are not in current ETC.
 
Is there any other interesting of these points?
 
Best regards,
Bui Quang Tuan